184 research outputs found
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
Spatial process models for analyzing geostatistical data entail computations
that become prohibitive as the number of spatial locations become large. This
manuscript develops a class of highly scalable Nearest Neighbor Gaussian
Process (NNGP) models to provide fully model-based inference for large
geostatistical datasets. We establish that the NNGP is a well-defined spatial
process providing legitimate finite-dimensional Gaussian densities with sparse
precision matrices. We embed the NNGP as a sparsity-inducing prior within a
rich hierarchical modeling framework and outline how computationally efficient
Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or
decomposing large matrices. The floating point operations (flops) per iteration
of this algorithm is linear in the number of spatial locations, thereby
rendering substantial scalability. We illustrate the computational and
inferential benefits of the NNGP over competing methods using simulation
studies and also analyze forest biomass from a massive United States Forest
Inventory dataset at a scale that precludes alternative dimension-reducing
methods
Multi-objective point cloud autoencoders for explainable myocardial infarction prediction
Myocardial infarction (MI) is one of the most common causes of death in the
world. Image-based biomarkers commonly used in the clinic, such as ejection
fraction, fail to capture more complex patterns in the heart's 3D anatomy and
thus limit diagnostic accuracy. In this work, we present the multi-objective
point cloud autoencoder as a novel geometric deep learning approach for
explainable infarction prediction, based on multi-class 3D point cloud
representations of cardiac anatomy and function. Its architecture consists of
multiple task-specific branches connected by a low-dimensional latent space to
allow for effective multi-objective learning of both reconstruction and MI
prediction, while capturing pathology-specific 3D shape information in an
interpretable latent space. Furthermore, its hierarchical branch design with
point cloud-based deep learning operations enables efficient multi-scale
feature learning directly on high-resolution anatomy point clouds. In our
experiments on a large UK Biobank dataset, the multi-objective point cloud
autoencoder is able to accurately reconstruct multi-temporal 3D shapes with
Chamfer distances between predicted and input anatomies below the underlying
images' pixel resolution. Our method outperforms multiple machine learning and
deep learning benchmarks for the task of incident MI prediction by 19% in terms
of Area Under the Receiver Operating Characteristic curve. In addition, its
task-specific compact latent space exhibits easily separable control and MI
clusters with clinically plausible associations between subject encodings and
corresponding 3D shapes, thus demonstrating the explainability of the
prediction
Modeling 3D cardiac contraction and relaxation with point cloud deformation networks
Global single-valued biomarkers of cardiac function typically used in
clinical practice, such as ejection fraction, provide limited insight on the
true 3D cardiac deformation process and hence, limit the understanding of both
healthy and pathological cardiac mechanics. In this work, we propose the Point
Cloud Deformation Network (PCD-Net) as a novel geometric deep learning approach
to model 3D cardiac contraction and relaxation between the extreme ends of the
cardiac cycle. It employs the recent advances in point cloud-based deep
learning into an encoder-decoder structure, in order to enable efficient
multi-scale feature learning directly on multi-class 3D point cloud
representations of the cardiac anatomy. We evaluate our approach on a large
dataset of over 10,000 cases from the UK Biobank study and find average Chamfer
distances between the predicted and ground truth anatomies below the pixel
resolution of the underlying image acquisition. Furthermore, we observe similar
clinical metrics between predicted and ground truth populations and show that
the PCD-Net can successfully capture subpopulation-specific differences between
normal subjects and myocardial infarction (MI) patients. We then demonstrate
that the learned 3D deformation patterns outperform multiple clinical
benchmarks by 13% and 7% in terms of area under the receiver operating
characteristic curve for the tasks of prevalent MI detection and incident MI
prediction and by 7% in terms of Harrell's concordance index for MI survival
analysis
Graphical Gaussian Process Models for Highly Multivariate Spatial Data
For multivariate spatial Gaussian process (GP) models, customary
specifications of cross-covariance functions do not exploit relational
inter-variable graphs to ensure process-level conditional independence among
the variables. This is undesirable, especially for highly multivariate
settings, where popular cross-covariance functions such as the multivariate
Mat\'ern suffer from a "curse of dimensionality" as the number of parameters
and floating point operations scale up in quadratic and cubic order,
respectively, in the number of variables. We propose a class of multivariate
"Graphical Gaussian Processes" using a general construction called "stitching"
that crafts cross-covariance functions from graphs and ensures process-level
conditional independence among variables. For the Mat\'ern family of functions,
stitching yields a multivariate GP whose univariate components are Mat\'ern
GPs, and conforms to process-level conditional independence as specified by the
graphical model. For highly multivariate settings and decomposable graphical
models, stitching offers massive computational gains and parameter dimension
reduction. We demonstrate the utility of the graphical Mat\'ern GP to jointly
model highly multivariate spatial data using simulation examples and an
application to air-pollution modelling
Graph-constrained Analysis for Multivariate Functional Data
Functional Gaussian graphical models (GGM) used for analyzing multivariate
functional data customarily estimate an unknown graphical model representing
the conditional relationships between the functional variables. However, in
many applications of multivariate functional data, the graph is known and
existing functional GGM methods cannot preserve a given graphical constraint.
In this manuscript, we demonstrate how to conduct multivariate functional
analysis that exactly conforms to a given inter-variable graph. We first show
the equivalence between partially separable functional GGM and graphical
Gaussian processes (GP), proposed originally for constructing optimal
covariance functions for multivariate spatial data that retain the conditional
independence relations in a given graphical model. The theoretical connection
help design a new algorithm that leverages Dempster's covariance selection to
calculate the maximum likelihood estimate of the covariance function for
multivariate functional data under graphical constraints. We also show that the
finite term truncation of functional GGM basis expansion used in practice is
equivalent to a low-rank graphical GP, which is known to oversmooth marginal
distributions. To remedy this, we extend our algorithm to better preserve
marginal distributions while still respecting the graph and retaining
computational scalability. The insights obtained from the new results presented
in this manuscript will help practitioners better understand the relationship
between these graphical models and in deciding on the appropriate method for
their specific multivariate data analysis task. The benefits of the proposed
algorithms are illustrated using empirical experiments and an application to
functional modeling of neuroimaging data using the connectivity graph among
regions of the brain.Comment: 23 pages, 6 figure
Multi-class point cloud completion networks for 3D cardiac anatomy reconstruction from cine magnetic resonance images
Cine magnetic resonance imaging (MRI) is the current gold standard for the
assessment of cardiac anatomy and function. However, it typically only acquires
a set of two-dimensional (2D) slices of the underlying three-dimensional (3D)
anatomy of the heart, thus limiting the understanding and analysis of both
healthy and pathological cardiac morphology and physiology. In this paper, we
propose a novel fully automatic surface reconstruction pipeline capable of
reconstructing multi-class 3D cardiac anatomy meshes from raw cine MRI
acquisitions. Its key component is a multi-class point cloud completion network
(PCCN) capable of correcting both the sparsity and misalignment issues of the
3D reconstruction task in a unified model. We first evaluate the PCCN on a
large synthetic dataset of biventricular anatomies and observe Chamfer
distances between reconstructed and gold standard anatomies below or similar to
the underlying image resolution for multiple levels of slice misalignment.
Furthermore, we find a reduction in reconstruction error compared to a
benchmark 3D U-Net by 32% and 24% in terms of Hausdorff distance and mean
surface distance, respectively. We then apply the PCCN as part of our automated
reconstruction pipeline to 1000 subjects from the UK Biobank study in a
cross-domain transfer setting and demonstrate its ability to reconstruct
accurate and topologically plausible biventricular heart meshes with clinical
metrics comparable to the previous literature. Finally, we investigate the
robustness of our proposed approach and observe its capacity to successfully
handle multiple common outlier conditions
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